Question

One mole of monoatomic ideal gas expands adiabatically at initial temperature $T$ against a constant external pressure of $1 atm$ from $1\, L$ to $2 \,L$. Find out the final temperature $\left(R=0.0821 \,L \,atm \,K ^{-1} \,mol ^{-1}\right)$

• A. $T$
• B. $\frac{T}{ (2)^{\frac{5}{3}-1}}$
• C. $T -\frac{2}{ 3 \times 0.082}$
• D. $T + \frac{2}{ 3 \times 0.082}$

Answer 1

Answer: (C)

For an irreversible, adiabatic process;
$0=C_{V}\left(T_{2}-T_{1}\right)+p_{e}\left(V_{2}-V_{1}\right)$
Substituting the values
$C_{V}\left(T-T_{2}\right)=1(2-1)$ atm $L$
$\Rightarrow T-T_{2}=\frac{1}{C_{V}}=\frac{2}{3 R}$
$ \Rightarrow T_{2}=T-\frac{2}{3 \times 0.082}$